Continuity mistake: Kenshin loses his sword battling with the guards at the beginning of the movie. The sword gets stuck almost horizontally in a tree stump. Then one of the guards grabs it as he rides by with his horse, but the katana is now stuck in the tree at a sharper angle which makes it possible to reach for it and grab it on the fly. (00:02:35)
Continuity mistake: When Benkei climbs the sewer ladder and disappears into the light, Donatello is touching the ladder in the first shot, in fact he puts both hands on deliberately, but he's not even touching it in the second. (01:28:35)
Continuity mistake: In the baffling phase when Whit takes exception to the killing if it's done by guns and Walker just throws him with the others, Elias Koteas moves his gun from the left to the right hand when Stuart Wilson calls for Niles, but in the next shot the gun is much lower. (01:18:15)
Continuity mistake: When the guard tells Norinaga about his honor guards; "They're coming! They're behind the wagon!", Norinaga's hand placement changes between shot and reverse. (00:28:15)
Answer: Michelangelo wants to stay behind for the same reasons as Raphael: because in that time and place, they are well respected, even revered as heroes. They can live openly and not be banished to sewers or subway stations.
LorgSkyegon
Mikey didn't want to stay behind because of Yoshi but because of Mitsu. Raphael even points out that she's the reason he doesn't want to return. When Mikey says they should stay, Raph responds, "Now, forget about Mitsu and give me the scepter."